Properties

Label 320.2.c
Level $320$
Weight $2$
Character orbit 320.c
Rep. character $\chi_{320}(129,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $4$
Sturm bound $96$
Trace bound $11$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 4 \)
Sturm bound: \(96\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(320, [\chi])\).

Total New Old
Modular forms 60 14 46
Cusp forms 36 10 26
Eisenstein series 24 4 20

Trace form

\( 10q + 2q^{5} - 10q^{9} + O(q^{10}) \) \( 10q + 2q^{5} - 10q^{9} - 8q^{21} + 2q^{25} + 4q^{29} - 12q^{41} + 30q^{45} - 2q^{49} + 20q^{61} + 16q^{65} - 72q^{69} + 18q^{81} - 32q^{85} - 28q^{89} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(320, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
320.2.c.a \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots\)
320.2.c.b \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots\)
320.2.c.c \(2\) \(2.555\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots\)
320.2.c.d \(4\) \(2.555\) \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(320, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)